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The IS/LM model is an interpretation of Keynes' General Theory (1936) by Hicks and Hansen (which never got the official stamp by Keynes, by the way).

Follow up:

There is a goods market equilibrium in which investments are equal to savings at the same time that demand is equal to supply. Imposing one condition on the model closes it so the other condition is also fulfilled. This part is called IS (investments=savings). Then, there is the monetary side in which money supply equals liquidity demand. Put the other way around, this part is called LM.

There are two reasons why people hold liquidity: to speculate and to execute transactions.

Now the problem I have with the depiction by Krugman is his investment equals savings schedule where you have the interest rate on the vertical axis. That does not belong to the IS/LM model. Savings is not a function of the interest rate, it rather depends on income (Y). Therefore, the graph which Krugman reproduces in his reply to Keen shows a loanable funds system: savings depend positively on the interest rate, and investment depends negatively on the interest rate. That is a cornerstone of neo-classical theory - and under no circumstances compatible with the IS/LM model.

In the IS/LM equilibrium, savings equal investment by assumption (either directly or indirectly, as I have described above). Note the order of the two: investment is given by the investment schedule (which depends on aggregate demand) in combination with the interest rate, and savings adjust to that. Hence there is no way that you can draw the diagram like Krugman did and say that this is IS/LM. Again, savings is not a function of the interest rate. Indirectly, a fall in the interest rate will cause a rise in investment, which creates higher incomes and therefore higher savings! So, a fall in the interest rate leads to a rise in savings. This is incompatible with Krugman's graph. He writes towards the end of his post:

In fact, that’s the essential insight of IS-LM: both liquidity preference and loanable funds are true, which is possible because both the interest rate and income are adjusting variables. Hicks could have told you that; in fact, he did.

The loanable funds theory says among other things that savings depend on the interest rate, but in the IS/LM model they depend on income only. The adjustment comes via income, not the interest rate. Given the amount of investment, the amount of savings adjust via the multiplier process which creates in change in incomes (on which savings depend).

It might be insightful to have a look at a corrected version of Krugman's diagram so that it shows what I believe is the IS/LM full employment equilibrium. Since savings depend on employment (S=s*Y), the variable is completely determined by the assumption that we are in full employment (Y=Y*). The given investment schedule does indeed depend on the interest rate, so the diagram should look like this:

Of course, the only way now to impose the equality of savings and investment is via a fall in income so that savings come down to the level of investment with an interest rate of zero. The level of income is below the level of full employment. Consider the disequilibrium mentioned by Keen:

"So where is the economy, in terms of the IS-LM diagram? It isn’t, as soon as you acknowledge that the economy is in disequilibrium, the IS-LM model can’t be used to represent it."

I always interpreted the IS/LM model as one of comparative statics. You can only compare equilibria; dynamics are not modeled, neither from non-equilibrium to equilibrium nor from one equilibrium to another.

(As always, some sloppy drawing in the IS/LM model on my part. The investment schedule should stop where it hits the savings schedule.)

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